Systems and methods for deep learning-based image reconstruction

ABSTRACT

Methods and systems for deep learning based image reconstruction are disclosed herein. An example method includes receiving a set of imaging projections data, identifying a voxel to reconstruct, receiving a trained regression model, and reconstructing the voxel. The voxel is reconstructed by: projecting the voxel on each imaging projection in the set of imaging projections according to an acquisition geometry, extracting adjacent pixels around each projected voxel, feeding the regression model with the extracted adjacent pixel data to produce a reconstructed value of the voxel, and repeating the reconstruction for each voxel to be reconstructed to produce a reconstructed image.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of priority to U.S.Non-Provisional patent application Ser. No. 15/720,632, filed on Sep.29, 2017, entitled “SYSTEMS AND METHODS FOR DEEP LEARNING-BASED IMAGERECONSTRUCTION”, which is herein incorporated by reference in itsentirety for all purposes.

FIELD OF THE DISCLOSURE

This disclosure relates generally to image reconstruction, and, moreparticularly, to systems and methods for deep learning-based imagereconstruction.

BACKGROUND

In recent years, digital breast tomosynthesis (DBT) andcontrast-enhanced digital breast tomosynthesis (CE-DBT) have proved tobe effective cancer detection techniques. DBT creates athree-dimensional (3D) image of the breast using x-rays. By takingmultiple x-ray pictures of each breast from many angles, a computer cangenerate a 3D image used to detect any abnormalities. A critical part ofthe DBT/CE-DBT process is image reconstruction as it directly impactsthe content of the data that the radiologists will review to determineany diagnosis. To reconstruct the image, algorithms trained and used toreduce the noise and any streak lines. Despite the complexity of thealgorithms, the DBT process typically results in non-perfect imagereconstruction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates an example diagram representing the reconstructionof a voxel using imaging projection data.

FIG. 1B illustrates an example diagram representing the reconstructionof a pixel using imaging projection data.

FIG. 1C illustrates an example diagram representing the reconstructionof a pixel using a given volume.

FIG. 2A illustrates an example diagram representing the reconstructionof a slab using imaging projection data.

FIG. 2B illustrates an example diagram representing the reconstructionof a slab using a given volume.

FIG. 3A is a system diagram to implement the diagrams of FIGS. 1A-2B toreconstruct a voxel with imaging projections.

FIG. 3B is a system diagram to implement the diagrams of FIGS. 1A-2B toreconstruct a pixel with imaging projections.

FIG. 3C is a system diagram to implement the diagrams of FIGS. 1A-2B toreconstruct a pixel with a given volume.

FIG. 3D is a system diagram to implement the diagrams of FIGS. 1A-2B toreconstruct a pixel with imaging projections and a given volume.

FIG. 3E is a system diagram to implement the diagrams of FIGS. 1A-2B toreconstruct a voxel within a slab with a given volume, a givenorientation parameter, and a given thickness parameter.

FIG. 4A illustrates an example implementation of the system diagram ofFIG. 3A.

FIG. 4B illustrates an example implementation of the system diagram ofFIG. 3B.

FIG. 4C illustrates an example implementation of the system diagram ofFIG. 3C.

FIG. 4D illustrates an example implementation of the system diagram ofFIG. 3D.

FIG. 4E illustrates an example implementation of the system diagram ofFIG. 3E.

FIG. 5 is a flowchart representative of an example method to reconstructan image.

FIG. 6 is a flowchart representative of an example method to choose atraining method to train a regression model.

FIG. 7 is a flowchart representative of an example method to use aregression model that is trained on a database composed of digitalanthropomorphic phantoms.

FIG. 8 is a flowchart representative of an example method to use aregression model that is trained on a database composed of computedtomography (CT) reconstructed data.

FIG. 9 is a flowchart representative of an example method to use aregression model that is trained on a database composed of imagingacquisitions that have been reconstructed with a given algorithm.

FIG. 10 is a flowchart representative of an example method to deploy aregression model.

FIG. 11 is a flowchart representative of an example method to use aregression model for reconstruction.

FIG. 12 is a flowchart representative of an example method to provide anoutput of a reconstructed image.

FIG. 13 is a processor diagram which can be used to implement themethods of FIGS. 1-12 .

The figures are not to scale. Instead, to clarify multiple layers andregions, the thickness of the layers may be enlarged in the drawings.Wherever possible, the same reference numbers will be used throughoutthe drawing(s) and accompanying written description to refer to the sameor like parts. As used in this patent, stating that any part (e.g., alayer, film, area, or plate) is in any way positioned on (e.g.,positioned on, located on, disposed on, or formed on, etc.) anotherpart, means that the referenced part is either in contact with the otherpart, or that the referenced part is above the other part with one ormore intermediate part(s) located there between. Stating that any partis in contact with another part means that there is no intermediate partbetween the two parts.

BRIEF SUMMARY

Certain examples provide methods and systems for deep learning basedimage reconstruction.

An example method disclosed herein includes receiving a set of imagingprojection data, identifying a voxel to reconstruct, and receiving atrained regression model. The example method further includesreconstructing the voxel by: projecting the voxel onto each imagingprojection in the set of projections according to an acquisitiongeometry, extracting adjacent pixels around each projected voxel,feeding the regression model with the extracted adjacent pixel data toproduce a reconstructed value of the reconstructed model, and repeatingthe reconstruction for each voxel to be reconstructed to produce areconstructed image.

An example system disclosed herein includes a regression model trainerto train a regression model, a voxel identifier to identify a voxel tobe reconstructed, an imaging projections data receiver to receive a setof imaging projections, and a voxel reconstructor. The voxelreconstructor includes a voxel projector to project the voxel onto eachimaging projection in the set of imaging projections according to anacquisition geometry, an adjacent pixel extractor to extract adjacentpixels around each projected voxel, and a regression model feeder tofeed the regression model with the extracted adjacent pixel data toproduce a reconstructed value of the voxel.

An example non-transitory computer readable storage medium disclosedherein includes instructions which, when executed, cause a machine to atleast receive a set of projections data, identify a voxel toreconstruct, receive a trained regression model, and reconstruct thevoxel by: projecting the voxel onto each imaging projection in the setof imaging projections according to an acquisition geometry, extractingadjacent pixels around each projected voxel, feeding the regressionmodel with the extracted adjacent pixel data to produce a reconstructedvalue of the voxel, and repeating the reconstruction for each voxel tobe reconstructed to produce a reconstructed image.

An example method disclosed herein includes receiving a set of imagingprojection data, identifying a pixel to reconstruct, receiving a trainedregression model, and reconstructing the pixel. Reconstructing the pixelincludes mapping the pixel onto each imaging projection in the set ofprojections according to an acquisition geometry, extracting adjacentpixels around each mapped pixel, feeding the regression model with theextracted adjacent pixel data to produce a reconstructed value of thepixel, and repeating the reconstruction for each pixel to bereconstructed.

An example system disclosed herein includes a regression model trainerto train a regression model, a pixel identifier to identify a pixel tobe reconstructed, an imaging projections data receiver to receive a setof imaging projections, and a pixel reconstructor. The pixelreconstructor includes a pixel mapper to map the pixel on each imagingprojection in the set of imaging projections according to an acquisitiongeometry, an adjacent pixel extractor to extract adjacent pixels aroundeach mapped pixel, and a regression model feeder to feed the regressionmodel with the extracted adjacent pixel data to produce a reconstructedvalue for the pixel.

An example non-transitory computer readable storage medium comprisinginstructions which, when executed, cause a machine to at least receive aset of imaging projection data, identify a pixel to reconstruct, receivea trained regression model, and reconstruct the pixel. Reconstructingthe pixel includes mapping the pixel on each imaging projection in theset of imaging projections according to an acquisition geometry,extracting adjacent pixels around each mapped pixel, feeding theregression model with the extracted adjacent pixel data to produce areconstructed value of the pixel, and repeating the reconstruction foreach pixel to be reconstructed.

An example method disclosed herein includes receiving a volume,identifying a pixel to reconstruct, receiving a trained regressionmodel, and reconstructing the pixel. Reconstructing the pixel includesmapping the pixel onto voxels from the volume according to anacquisition geometry, extracting adjacent voxels around each mappedpixel, feeding the regression model with the extracted adjacent voxeldata to produce a reconstructed value of the pixel, and repeating thereconstruction for each pixel to be reconstructed.

An example system disclosed herein includes a regression model trainerto train a regression model, a pixel identifier to identify a pixel tobe reconstructed, a volume receiver to receive a volume, and a pixelreconstructor. The pixel reconstructor includes a pixel mapper to mapthe pixel onto voxels from the volume according to an acquisitiongeometry, an adjacent voxel extractor to extract adjacent voxels aroundeach mapped pixel, and a regression model feeder to feed the regressionmodel with the extracted adjacent voxel data to produce a reconstructedvalue for the pixel.

An example non-transitory computer readable storage medium comprisinginstructions which, when executed, cause a machine to at least receive avolume, identify a pixel to reconstruct, receive a trained regressionmodel, and reconstruct the pixel. Reconstructing the pixel includesmapping the pixel onto voxels from the volume according to anacquisition geometry, extracting adjacent voxels around each mappedpixel, feeding the regression model with the extracted adjacent voxeldata to produce a reconstructed value of the pixel, and repeating thereconstruction for each pixel to be reconstructed.

An example method disclosed herein includes receiving a set of imagingprojection data, receiving a volume, identifying a pixel to reconstruct,receiving a trained regression model, and reconstructing the pixel.Reconstructing the pixel includes mapping the pixel onto each imagingprojection in the set of projections according to an acquisitiongeometry, mapping the pixel onto voxels from the volume according to anacquisition geometry, extracting adjacent pixels around each mappedpixel in the projections, extracting adjacent voxels around each mappedpixel in the volume, feeding the regression model with the extractedadjacent pixel data and extracted adjacent voxel data to produce areconstructed value of the pixel, and repeating the reconstruction foreach pixel to be reconstructed.

An example system disclosed herein includes a regression model trainerto train a regression model, a pixel identifier to identify a pixel tobe reconstructed, an imaging projections data receiver to receive a setof imaging projections, a volume receiver to receive a volume and apixel reconstructor. The pixel reconstructor includes a pixel mapper tomap the pixel on each imaging projection in the set of imagingprojections according to an acquisition geometry and to map the pixelonto voxels from the volume according to an acquisition geometry, anadjacent pixel extractor to extract adjacent pixels around each mappedpixel in the imaging projections, an adjacent voxel extractor to extractadjacent voxels around the mapped pixel in the volume, and a regressionmodel feeder to feed the regression model with the extracted adjacentpixel data and the extracted adjacent voxel data to produce areconstructed value for the pixel.

An example non-transitory computer readable storage medium comprisinginstructions which, when executed, cause a machine to at least receive aset of imaging projection data, receive a volume, identify a pixel toreconstruct, receive a trained regression model, and reconstruct thepixel. Reconstructing the pixel includes mapping the pixel on eachimaging projection in the set of imaging projections according to anacquisition geometry, mapping the pixel onto voxels from the volumeaccording to an acquisition geometry, extracting adjacent pixels aroundeach mapped pixel in the projections, extracting adjacent voxels aroundthe mapped pixel in the volume, feeding the regression model with theextracted adjacent pixel data to produce a reconstructed value of thepixel, and repeating the reconstruction for each pixel to bereconstructed.

An example method disclosed herein includes receiving a volume,receiving an orientation parameter and a thickness parameter for a slabto reconstruct, identifying a voxel from the slab to reconstruct,receiving a trained regression model, and reconstructing the voxel.Reconstructing the voxel includes mapping the voxel from the slab voxelsfrom the volume according to the orientation parameter and the thicknessparameter of the slab, extracting adjacent voxels from the volume aroundeach mapped voxel from the slab, feeding the regression model with theextracted adjacent voxel from the volume data to produce a reconstructedvalue of the voxel from the slab, and repeating the reconstruction foreach voxel from the slab to be reconstructed.

An example system disclosed herein includes a regression model trainerto train a regression model, a volume receiver to receive a volume, anorientation parameter receiver to receive an orientation parameter for aslab to reconstruct, a thickness parameter receiver to receive athickness parameter for a slab to reconstruct, a voxel identifier toidentify a voxel from the slab to be reconstructed, and a voxelreconstructor. The voxel reconstructor includes a voxel mapper to mapthe voxel from the slab onto voxels from the volume according to theorientation parameter and the thickness parameter of the slab, anadjacent voxel extractor to extract adjacent voxels from the volumearound each mapped voxel from the slab, and a regression model feeder tofeed the regression model with the extracted adjacent voxel from thevolume data to produce a reconstructed value of the voxel from the slab.

An example non-transitory computer readable storage medium comprisinginstructions which, when executed, cause a machine to at least receive avolume, receive an orientation parameter and a thickness parameter for aslab to reconstruct, identify a voxel from the slab to reconstruct,receive a trained regression model, and reconstruct the voxel.Reconstructing the voxel includes mapping the voxel from the slab ontovoxels from the volume according to the orientation parameter and thethickness parameter of the slab, extracting adjacent voxels from thevolume around each mapped voxel from the slab, feeding the regressionmodel with the extracted adjacent voxel from the volume data to producea reconstructed value of the voxel from the slab, and repeating thereconstruction for each voxel from the slab to be reconstructed.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings that form a part hereof, and in which is shown byway of illustration specific examples that may be practiced. Theseexamples are described in sufficient detail to enable one skilled in theart to practice the subject matter, and it is to be understood thatother examples may be utilized. The following detailed description istherefore, provided to describe an exemplary implementation and not tobe taken limiting on the scope of the subject matter described in thisdisclosure. Certain features from different aspects of the followingdescription may be combined to form yet new aspects of the subjectmatter discussed below.

When introducing elements of various embodiments of the presentdisclosure, the articles “a,” “an,” “the,” and “said” are intended tomean that there are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

As used herein, the terms “system,” “unit,” “module,” etc., may includea hardware and/or software system that operates to perform one or morefunctions. For example, a module, unit, or system may include a computerprocessor, controller, and/or other logic-based device that performsoperations based on instructions stored on a tangible and non-transitorycomputer readable storage medium, such as a computer memory.Alternatively, a module, unit, or system may include a hard-wired devicethat performs operations based on hard-wired logic of the device.Various modules, units, engines, and/or systems shown in the attachedfigures may represent the hardware that operates based on software orhard-wired instructions, the software that directs hardware to performthe operations, or a combination thereof.

As used herein, the term “mapping” indicates translating a position of alocation in an object being imaged to a corresponding location in one ormore images obtained of the object. Alternatively or in addition,mapping can refer to a correlation between common points in a pluralityof images or views such that a point in a first image is mapped to thesame point in other related images such that their location coordinatesare correlated when forming a synthetic two-dimensional image,three-dimensional volume, etc. For example, each element (e.g. a pixel,a voxel, etc.) in a 3D object has a location on a coordinate system.Mapping the elements in the 3D object indicates translating a data pointfrom the 3D object to a corresponding data point in a generated 2D or 3Dimage.

As used herein, the term “projection” or “projection image” indicates animage obtained from emission of x-rays from a particular angle or view.A projection can be thought of as a particular example of mapping inwhich a set of projection images are captured from different angles of a3D object and mapped or combined/fused to reconstruct a volume and/orcreate a synthetic 2D image. Each projection image is captured relativeto a central projection (e.g. base projection, straight-on projection,zero angle projection, etc.). The resulting image from the projectionsis either a 3D reconstructed image that is approximately identical tothe original 3D object or a synthetic 2D image that merges eachprojection together and benefits from the information in each view.

As used herein, the term “acquisition geometry” is a particular path ormovement of an x-ray source with respect to a 3D object (e.g., detector)to obtain a series of 2D projections.

While certain examples are described below in the context of medical orhealthcare workplaces, other examples can be implemented outside themedical environment.

In many different applications, deep learning techniques have utilizedlearning methods that allow a machine to be given raw data and determinethe representations needed for data classification. Deep learningascertains structure in data sets using back propagation algorithmswhich are used to alter internal parameters (e.g., node weights) of thedeep learning machine. Deep learning machines can utilize a variety ofmultilayer architectures and algorithms. While machine learning, forexample, involves an identification of features to be used in trainingthe network, deep learning processes raw data to identify features ofinterest without the external identification.

Deep learning in a neural network environment includes numerousinterconnected nodes referred to as neurons. Input neurons, activatedfrom an outside source, activate other neurons based on connections tothose other neurons which are governed by the machine parameters. Aneural network behaves in a certain manner based on its own parameters.Learning refines the machine parameters, and, by extension, theconnections between neurons in the network, such that the neural networkbehaves in a desired manner.

Deep learning operates on the understanding that many datasets includehigh level features which include low level features. While examining animage, for example, rather than looking for an object, it is moreefficient to look for edges which form motifs which form parts, whichform the object being sought. These hierarchies of features can be foundin many different forms of data such as speech and text, etc.

An example use of deep learning techniques in the medical field ismammography. Mammography is used to screen for breast cancer and otherabnormalities. Traditionally, mammograms have been formed on x-ray film.However, more recently, flat panel digital imagers have been introducedthat acquire a mammogram in digital form, and thereby facilitateanalysis and storage of the acquired images. Further, substantialattention and technological development have been dedicated towardobtaining three-dimensional images of the breast. Three-dimensional (3D)mammography is also referred to as digital breast tomosynthesis (DBT).Two-dimensional (2D) mammography is full-field digital mammography, andsynthetic 2D mammography produces 2D pictures derived from 3D data bycombining individual enhanced slices (e.g., 1 mm, 2 mm, etc.) of a DBTvolume. Breast tomosynthesis systems construct a 3D image volume from aseries of two-dimensional (2D) projection images, each projection imageobtained at a different angular displacement of an x-ray source. Theconstructed 3D image volume is typically presented as a plurality ofslices of image data, the slices being geometrically reconstructed onplanes parallel to the imaging detector.

Example Systems and Associated Methods

FIG. 1A illustrates an example diagram 100 representing thereconstruction of a voxel 102 using imaging projection data. The voxel102 within a 3D space 104 is to be reconstructed. The voxel 102 isprojected into a first 2D projected view 106, a second 2D projected view108, and a third 2D projected view 110, each 2D projection representinga slice 112 of the voxel 102. Each 2D projected view 106, 108, 110 has aunique image value and position indicator. For example, the first 2Dprojected view 106 may have a unique image value of six and representthe top of the voxel 102. In the same example, the second 2D projectedview 108 may have a unique image value of nine and represent the bottomof the voxel 102. Still further in the same example, the third 2Dprojected view 110 may have a unique image value of five and represent aside of the voxel 102. In this example, there are three 2D projectedviews. However, in other examples, there may be any number of 2Dprojected views, each 2D projected view representing an image slice 112of the volume. The 2D projected views 106, 108, 110 provide an input fora regression model 114. This input for a regression model 114 is used toreconstruct 116 the voxel 102 to an approximately identical voxel. Theprocess that the diagram 100 describes repeats until each voxel 102within the 3D space 104 has been reconstructed. In this example, a voxelis being reconstructed. However, in other examples, any graphicalelement may be reconstructed (e.g., a pixel, a slab, etc.).

FIG. 1B illustrates an example diagram 120 representing thereconstruction of a pixel 122 within an image 124 using imagingprojection data. While the voxel 102 of FIG. 1A is projected ontoimaging projections, in this example, the pixel 122 is mapped 126 ontoeach imaging projection 128 in the set of projections according to anacquisition geometry. The mapping 126 of the pixel 122 results in anapproximately identical pixel 130 on the imaging projection 128.

FIG. 1C illustrates an example diagram 140 representing thereconstruction of a pixel 142 within an image 144 using a given volume146. In this example, the pixel 142 is mapped 148 onto a voxel 150 fromthe volume according to an acquisition geometry. The view of the pixel142 in the 2D image 144 is extrapolated to provide a representation ofthe voxel 150 in the volume 146, for example.

FIG. 2A illustrates an example diagram 200 representing thereconstruction of a slab 202 using imaging projection data. The slab 202made of several voxels 204 within a 3D space 206 is to be reconstructed.In this illustrated example, the slab 202 is projected onto a first 2Dprojected view 208, a second 2D projected view 210, and a third 2Dprojected view 212, each 2D projected view representing a slice 214 ofeach voxel 204 in the slab 202. The first 2D projected view 208, thesecond 2D projected view 210, and the third 2D projected view 212 eachhave a unique image value and a projected image value. The projectedimage value 214 of the second 2D projected view 210 is identical to theunique image value 216 because the second 2D projected view 210 containsa base image value 218. In this example, the second 2D projected view210 contains the base image value 218. However, in other examples, anyone of the 2D projected views may contain the base image value. Theprojected image value 220 of the first 2D projected view 208 representsthe distance of the unique image value 222 of the first 2D projectedview 208 from the base image value 216. Similarly, the projected imagevalue 224 of the third 2D projected view 212 represents the distance ofthe unique image value 226 of the third 2D projected view 212 from thebase image value 216. For example, if the base image value 216 of thesecond 2D projection is 8; the unique image value 222 of the first 2Dprojection 208 is 10; and the unique image value 226 of the third 2Dprojection 212 is 6, then the projected image value 220 of the first 2Dprojection 208 is +2 and the projected image value 224 of the third 2Dprojection 212 is −2. In this example, the unique image values arerelatively small, however in other examples they may be much longerwhich increases computational time and complexity.

Further illustrated in FIG. 2A is a base pixel 228 located in the 2Dprojected view that contains the base image value 218. In this example,the base pixel 228 is located in the second 2D projected view 210. FIG.2A also includes lines 230, 232 on each 2D projected view thatcorrespond to other views of the base pixel 228 (e.g., projection imagesacquired from different angles of the x-ray source with respect to thedetector). In this example, the lines 230, 232 are located on the first2D projected view 208 and the third 2D projected view 212. The lines230,232 correspond to the base pixel 228 in the second 2D projected view210 from different angles. Thus, the pixel 228 can appear as a point ina first view 210 but appear as a line 230, 232 or value with depth inother views 208, 212, for example. These locations can be mapped so thatthe correspondence is determined when generating a synthetic 2D image,3D reconstructed image, etc.

Furthermore, in this example, there are only three 2D projected views,while in other examples there may be many more 2D projected views basedon how many voxels 204 are in the slab 202, each 2D projected viewcorresponding to a slice 214 of the voxel 204. This further increasescomputational time and complexity. By using projected image valuesinstead of unique image values for each 2D projected view, computationaltime and complexity are decreased. The amount of memory required tostore the image values is also decreased.

Further illustrated in FIG. 2 is an input for a regression model 234provided by the 2D projected views 208, 210, 212. The input for aregression model 234 is then used to reconstruct 236 each voxel 204within the slab 202 to an approximately identical voxel and, as aresult, create an approximately identical slab. The process that thediagram 200 describes repeats until each voxel 204 within the slab 202has been reconstructed. In this example, the slab 202 that wasreconstructed is composed of voxels. However, in other examples, theslab may be composed of any type of graphical element (e.g., pixels,etc.).

FIG. 2B illustrates an example diagram representing the reconstructionof a slab 252 within a 3D space 254 using a given volume 256. While theslab 202 in FIG. 2A is projected onto a set of imaging projections, inthis example, the slab 252 is mapped 258 onto the volume 256 to createan approximately identical slab 260.

For example, a 3D geometry can be projected to a 2D surface at aparticular viewpoint. Thus, a 3D volume can be represented using a setof 2D views from image projections at different angles of the initialgeometry. The 2D projections may include lines that correspond to pixelsin other 2D projections.

In certain examples, a point can be selected and/or determined in a viewfor which a pixel is to be generated, and that point is mapped into aset of pixels in each associated individual view. A point in a targetimage view can correspond to a line in an adjacent image projection, forexample (see, e.g., FIG. 2A in which a point in the central image is apixel that is mapped to lines in the two other projection views). In aprojection image, a pixel is mapped to a voxel used to generate theprojection, for example.

Thus, image data with respect an object (e.g., a breast, etc.) can beused to begin with a voxel element of projection to determine where thevoxel maps on another projection. In certain examples, beginning with apixel in an image projection, voxels from which that pixel can originateare determined (e.g., go from projection to volume). In certainexamples, starting from a pixel in a first projection, correspondingpixel(s) in other projection(s) can be identified. In certain examples,a voxel can be mapped to voxels in adjacent slices to compute a slab.Thus, a volume can be reconstructed in a 3D image and/or a synthetic 2Dimage can be created from the projection views and correlations betweenpixel, voxel, etc.

FIGS. 3A-3E are example systems 300 to reconstruct images such as theexamples shown in FIGS. 1A-2B. The example system 300 includes areconstruction controller 301. The reconstruction controller 301initiates a reconstruction process such as example process(es) describedin further detail below. The reconstruction controller 301 may alsodecide which method is best to train a regression model at a trainingmodel 302 which is described in further detail in FIGS. 4A-4E. Theexample system 300 further includes a deployed model 304 within areconstructor 306. The deployed model 304 is a regression model that hasbeen trained at the training model 302. The reconstructor 306 isdescribed in further detail in FIGS. 4A-4E. FIGS. 3A-3E further includea computer workstation 308 encompassing the reconstructor 306 and thedeployed model 304. In this example, the training and reconstructing ofthe regression model are occurring at two different locations. However,in other examples, the training and reconstructing of the regressionmodel may occur at the same location. The computer workstation 308receives the deployed model 304 from the training model block 302. Thecomputer workstation 308 also receives a pixel, a voxel, and/or a slabto reconstruct, as well as data that is used to reconstruct the pixel,the voxel, and/or the slab. In the example of FIG. 3A, the computerworkstation 308 receives imaging projections 310 to reconstruct a voxel312. In the example of FIG. 3B, the computer workstation 308 receivesimaging projections 310 to reconstruct a pixel 314. In the example ofFIG. 3C, the computer workstation 308 receives a volume 316 toreconstruct a pixel 314. In the example of FIG. 3D, the computerworkstation 308 receives both imaging projections 310 and a volume 316to reconstruct a pixel 314. In the example of FIG. 3E, the computerworkstation 308 receives a volume 316, an orientation parameter 318, anda thickness parameter 320 to reconstruct a voxel 314 that is within aslab. While FIGS. 3A-3E are illustrated separately, in certain examplesFIGS. 3A-3E can be combined and implemented as a single systemaccommodating a plurality of graphic elements such as voxels, pixels,etc., for 2D and/or 3D image generation.

FIGS. 4A-4E illustrate an example implementation of the system 300 ofFIGS. 3A-3E described in further detail. The example system 300 includesthe reconstruction controller 301 of FIGS. 3A-3E. The example furtherillustrates a regression model trainer 402 which is located in thetraining model block 302 of FIGS. 3A-3E. The regression model trainer402 includes a digital anthropomorphic phantom (DAP) modeler 404, acomputed tomography (CT) modeler 406, and an algorithm modifier 408. TheDAP modeler 404 includes a DAP acquisition simulator 410, whichsimulates acquisitions based on digital anthropomorphic phantoms takenfrom a DAP database 412. The anthropomorphic phantoms act as models of aperfect reconstruction. The DAP modeler further includes a DAP algorithmcreator 414, wherein the regression model creates a new algorithmdifferent than existing reconstruction algorithms.

As illustrated in FIGS. 4A-4E, the CT modeler 406 includes a CTacquisition simulator 416, which uses CT reconstructed data as a modelof a perfect reconstruction to simulate acquisitions. The CTreconstructed data is stored in a CT database 418 within the CT modeler406. The CT modeler 406 further includes a CT algorithm creator 420,which allows the regression model to create a new algorithm differentthan existing reconstruction algorithms based on the CT reconstructiondata.

The algorithm modifier 408 of FIGS. 4A-4E includes an algorithm database422 including acquisitions that have been reconstructed with analgorithm in an algorithm reconstructor 424. The reconstructed algorithmmanages noise artifacts in an image to give high image quality. Aregression model that is trained in the algorithm modifier 408 decreasescomputation time and computational complexity of the reconstructedalgorithm.

The regression model trainer 402 instructs the DAP modeler 404, the CTmodeler 406, and the algorithm modifier 408 to perform the respectivetraining techniques if the appropriate information can be accessed bythe respective modeler 404, 406, 408. For example, if the regressionmodel trainer 402 receives a regression model for which only DAPs areavailable to the regression model trainer 402, then the DAP modeler 404performs the regression model training. However, in other examples, morethan one of the DAP modeler 404, the CT modeler 406, and the algorithmmodifier 408 may have information for a given regression model. In suchexamples, each of the DAP modeler 404, the CT modeler 406, and thealgorithm modifier 408 that has the appropriate information performs theregression model training. In such examples, the reconstructioncontroller 301 can select a result based on one or more criterion suchas highest accuracy percentage, fastest response time, etc.

Further illustrated in FIGS. 4A-4E is a type of receiver to receive datafor reconstruction along with an identifier to identify which element isto be reconstructed. The example of FIG. 4A includes an imagingprojections data receiver 430, which receives a set of imagingprojections 310 (FIG. 3 ) and sends the set of imaging projections 310to a voxel reconstructor 434 located within the reconstructor 306.Further illustrated in FIG. 4A is a voxel identifier 432 to identify thevoxel 312 (FIGS. 3A-3E) to be reconstructed and give the voxel 312 tothe voxel reconstructor 434. The example of FIG. 4B includes an imagingprojections data receiver 430, which receives a set of imagingprojections 310 (FIG. 3 ) and sends the set of imaging projections 310to a pixel reconstructor 452 located within the reconstructor 306.Further illustrated in FIG. 4A is a pixel identifier 450 to identify thepixel 314 (FIG. 3 ) to be reconstructed and give the pixel 314 to thepixel reconstructor 452. The example of FIGS. 4C and 4D include animaging projections data receiver 430, which receives a set of imagingprojections 310 (FIG. 3 ) and sends the set of imaging projections 310to a pixel reconstructor 452 located within the reconstructor 306. FIGS.4C and 4D further include a volume receiver 456 to receive the volume316 and send it to the pixel reconstructor 452. Further illustrated inFIGS. 4C and 4D is a pixel identifier 450 to identify the pixel 314(FIG. 3 ) to be reconstructed and give the pixel 314 to the pixelreconstructor 452. The example of FIG. 4E includes an orientationparameter receiver 460 to receive the orientation parameter 318 and athickness parameter receiver 462 to receive the thickness parameter 320.The orientation parameter 318 and the thickness parameter 320 are sentto a voxel reconstructor 434. Further illustrated in FIG. 4E is a voxelidentifier 432 to identify the voxel 312 (FIG. 3 ) to be reconstructedand give the voxel 312 to the voxel reconstructor 434.

The reconstructor 306 of FIGS. 4A-4E includes elements to reconstructthe given voxel 312 or pixel 314. The voxel reconstructor 434 of FIG. 4Aincludes a voxel projector 436 to project the voxel 312 on each of theset of 2D projections 208, 210, 212 of FIG. 2 according to anacquisition geometry; an adjacent pixel extractor 438 to extractadjacent pixels around each projected voxel 312; and a regression modelfeeder 440 to feed the regression model with the extracted adjacentpixel data. The pixel reconstructor 452 of FIGS. 4B and 4C includes apixel mapper 454 to map the pixel 314 onto each imaging projection ofthe set of projections according to an acquisition geometry; an adjacentpixel extractor 438 to extract adjacent pixels around each mapped pixel314; and a regression model feeder 440 to feed the regression model withthe extracted adjacent pixel data. The pixel reconstructor 452 of FIG.4D includes a pixel mapper 454 to map the pixel 314 onto each imagingprojection of the set of projections according to an acquisitiongeometry; an adjacent pixel extractor 438 to extract adjacent pixelsaround each mapped pixel 314 in the projections; an adjacent voxelextractor 458 to extract adjacent voxels around each mapped pixel 314 ina volume; and a regression model feeder 440 to feed the regression modelwith the extracted adjacent pixel data and extracted adjacent voxeldata. The voxel reconstructor 434 of FIG. 4E includes a voxel mapper 464to map the voxel 312 onto voxels from the volume 316 according to theorientation parameter 318 and the thickness parameter 320 of the slabfrom which the voxel 312 originated; an adjacent voxel extractor 458 toextract adjacent voxels around each mapped voxel 312; and a regressionmodel feeder 440 to feed the regression model with the extractedadjacent voxel data. The data from the either voxel reconstructor 434 orthe pixel reconstructor 452 of FIGS. 4A-4E is sent to a reconstructedvalue producer 442 which produces a reconstructed value of thereconstructed pixel or the reconstructed voxel (e.g., a gray value,etc.). The reconstructed value is received by a reconstructed imageproducer 444, which produces a reconstructed image based on thereconstructed values. The imaging projections data receiver 430, thevolume receiver 456, the voxel identifier 432, the pixel identifier 450,the orientation parameter receiver 460, the thickness parameterreceiver, the voxel reconstructor 434, the pixel reconstructor 452, thereconstructed value producer 442, and the reconstructed image producer444 are part of the computer workstation 308 of FIG. 3 .

The computer workstation 308 also includes a feedback generator 448. Thefeedback generator 448 identifies if a possible mistake has been made inthe reconstructed image. The reconstructed image producer 444 sends thereconstructed image to the user interface for a user to view. Forexample, if every reconstructed graphical element 312 within areconstructed image is a dark color except one outlier that is a lightor bright color, the disparity in color/intensity may be an indicationof a mistake made by either the regression model trainer 402 or thereconstructor 306. In such examples, the feedback generator 448communicates to the regression model trainer 402 to choose a differentmethod of the DAP modeler 404, the CT modeler 406, and the algorithmmodifier 408 to re-train the regression model. For example, if aregression model was trained using DAPs in the DAP modeler 404 thefeedback generator 448 indicates that a mistake may have been made, thenthe feedback generator 448 communicates to the regression model trainer402 that the regression model is to be re-trained on either the CTmodeler 406 or the algorithm modifier 408. In such an example, theaccuracy percentage for the DAP modeler 404 would decrease. As a result,the reconstruction controller 301 may be less likely to select the DAPmodeler 404 to train a regression model if the regression model trainer402 has information for more than one method to train the regressionmodel.

The computer workstation 308 further includes a user interface 449. Thereconstructed image producer 444 sends the reconstructed image to theuser interface 449 to be viewed by a user. In some examples, thereconstructed image may not be available to the user until the feedbackgenerator 448 decides that there are not any mistakes within thereconstructed image. However, in other examples, the user interface 449may display the reconstructed image immediately after it is produced bythe reconstructed image producer 444. In such examples, if the feedbackgenerator 448 indicates that a mistake has been made, the user interface449 may display the first reconstructed image until the second, moreaccurate, reconstructed image has been produced.

While an example manner of implementing the example system 300 of FIGS.4A-4E is illustrated in FIGS. 5-12 , one or more of the elements,processes and/or devices illustrated in FIGS. 3A-4E may be combined,divided, re-arranged, omitted, eliminated and/or implemented in anyother way. For example, while FIGS. 4A-4E are illustrated separately, incertain examples FIGS. 4A-4E can be combined and implemented as a singlesystem accommodating a plurality of graphic elements such as voxels,pixels, etc., for 2D and/or 3D image generation. Further, the examplereconstruction controller 301, the example regression model trainer 402which can, in some examples, contain the example digital anthropomorphicphantom modeler 404 which can, in some examples, contain the example DAPacquisition simulator 410, the example DAP database 412, and the examplealgorithm creator 414; the example CT modeler 406 which can, in someexamples contain the example CT acquisition simulator 416, the exampleCT database 418, and the example CT algorithm creator 420; the examplealgorithm modifier 408 which can, in some examples contain the examplealgorithm database 422 and the example acquisition reconstructor 424;the example imaging projections data receiver 430, the example volumereceiver 456, the example orientation parameter receiver 460, theexample thickness parameter receiver 462, the example pixel identifier450, the example voxel identifier 432, the example reconstructor 306which can, in some examples include the example voxel reconstructor 434which can, in some examples, contain the example voxel projector 436,the example adjacent pixel extractor 438, the example regression modelfeeder 440, the example voxel mapper 464, and the example adjacent voxelextractor 458; the example pixel reconstructor 452 which can, in someexamples, contain the example pixel mapper 454, the example adjacentpixel extractor 438, the example regression model feeder 440, and theexample adjacent voxel extractor 458; the example reconstructed valueproducer 442, and the example feedback generator 448 and/or, moregenerally, the example system 300 of FIGS. 4A-4E may be implemented byhardware, software, firmware and/or any combination of hardware,software and/or firmware. Thus, for example, any of the examplereconstruction controller 301, the example regression model trainer 402which can, in some examples, contain the example digital anthropomorphicphantom modeler 404 which can, in some examples, contain the example DAPacquisition simulator 410, the example DAP database 412, and the examplealgorithm creator 414; the example CT modeler 406 which can, in someexamples contain the example CT acquisition simulator 416, the exampleCT database 418, and the example CT algorithm creator 420; the examplealgorithm modifier 408 which can, in some examples contain the examplealgorithm database 422 and the example acquisition reconstructor 424;the example imaging projections data receiver 430, the example volumereceiver 456, the example orientation parameter receiver 460, theexample thickness parameter receiver 462, the example pixel identifier450, the example voxel identifier 432, the example reconstructor 306which can, in some examples include the example voxel reconstructor 434which can, in some examples, contain the example voxel projector 436,the example adjacent pixel extractor 438, the example regression modelfeeder 440, the example voxel mapper 464, and the example adjacent voxelextractor 458; the example pixel reconstructor 452 which can, in someexamples, contain the example pixel mapper 454, the example adjacentpixel extractor 438, the example regression model feeder 440, and theexample adjacent voxel extractor 458; the example reconstructed valueproducer 442, the example reconstructed image producer 444, the examplefeedback generator 448 and/or, more generally, the example system 300 ofFIGS. 4A-4E can be implemented by one or more analog or digitalcircuit(s), logic circuits, programmable processor(s), applicationspecific integrated circuit(s) (ASIC(s)), programmable logic device(s)(PLD(s)) and/or field programmable logic device(s) (FPLD(s)). Whenreading any of the apparatus or system claims of this patent to cover apurely software and/or firmware implementation, at least one of theexample reconstruction controller 301, the example regression modeltrainer 402 which can, in some examples, contain the example digitalanthropomorphic phantom modeler 404 which can, in some examples, containthe example DAP acquisition simulator 410, the example DAP database 412,and the example algorithm creator 414; the example CT modeler 406 whichcan, in some examples contain the example CT acquisition simulator 416,the example CT database 418, and the example CT algorithm creator 420;the example algorithm modifier 408 which can, in some examples containthe example algorithm database 422 and the example acquisitionreconstructor 424; the example imaging projections data receiver 430,the example volume receiver 456, the example orientation parameterreceiver 460, the example thickness parameter receiver 462, the examplepixel identifier 450, the example voxel identifier 432, the examplereconstructor 306 which can, in some examples include the example voxelreconstructor 434 which can, in some examples, contain the example voxelprojector 436, the example adjacent pixel extractor 438, the exampleregression model feeder 440, the example voxel mapper 464, and theexample adjacent voxel extractor 458; the example pixel reconstructor452 which can, in some examples, contain the example pixel mapper 454,the example adjacent pixel extractor 438, the example regression modelfeeder 440, and the example adjacent voxel extractor 458; the examplereconstructed value producer 442, the example reconstructed imageproducer 444, and the example feedback generator 448 and/or, moregenerally, the example system 300 of FIGS. 4A-4E is/are hereby expresslydefined to include a tangible computer readable storage device orstorage disk such as a memory, a digital versatile disk (DVD), a compactdisk (CD), a Blu-ray disk, etc. storing the software and/or firmware.Further still, the example system 300 of FIGS. 4A-4E may include one ormore elements, processes and/or devices in addition to, or instead of,those illustrated in FIGS. 4A-4E, and/or may include more than one ofany or all of the illustrated elements, processes and devices.

A flowchart representative of example machine readable instructions forimplementing the example system 300 of FIGS. 4A-4E is shown in FIGS.5-12 . In this example, the machine readable instructions comprise aprogram for execution by a processor such as the processor 1312 shown inthe example processor platform 1300 discussed below in connection withFIGS. 5-12 . The program may be embodied in software stored on atangible computer readable storage medium such as a CD-ROM, a floppydisk, a hard drive, a digital versatile disk (DVD), a Blu-ray disk, or amemory associated with the processor 1312, but the entire program and/orparts thereof could alternatively be executed by a device other than theprocessor 1312 and/or embodied in firmware or dedicated hardware.Further, although the example program is described with reference to theflowchart illustrated in FIGS. 5-12 , many other methods of implementingthe example system 300 may alternatively be used. For example, the orderof execution of the blocks may be changed, and/or some of the blocksdescribed may be changed, eliminated, or combined.

As mentioned above, the example processes of FIGS. 5-12 may beimplemented using coded instructions (e.g., computer and/or machinereadable instructions) stored on a tangible computer readable storagemedium such as a hard disk drive, a flash memory, a read-only memory(ROM), a compact disk (CD), a digital versatile disk (DVD), a cache, arandom-access memory (RAM) and/or any other storage device or storagedisk in which information is stored for any duration (e.g., for extendedtime periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm tangible computer readable storage medium is expressly defined toinclude any type of computer readable storage device and/or storage diskand to exclude propagating signals and to exclude transmission media. Asused herein, “tangible computer readable storage medium” and “tangiblemachine readable storage medium” are used interchangeably. Additionallyor alternatively, the example processes of FIGS. 5-12 may be implementedusing coded instructions (e.g., computer and/or machine readableinstructions) stored on a non-transitory computer and/or machinereadable medium such as a hard disk drive, a flash memory, a read-onlymemory, a compact disk, a digital versatile disk, a cache, arandom-access memory and/or any other storage device or storage disk inwhich information is stored for any duration (e.g., for extended timeperiods, permanently, for brief instances, for temporarily buffering,and/or for caching of the information). As used herein, the termnon-transitory computer readable medium is expressly defined to includeany type of computer readable storage device and/or storage disk and toexclude propagating signals and to exclude transmission media. As usedherein, when the phrase “at least” is used as the transition term in apreamble of a claim, it is open-ended in the same manner as the term“comprising” is open ended.

FIG. 5 is a flowchart representative of an example method 500 to producea reconstructed image. The example method 500 begins at block 502 wherethe regression model trainer 402 trains a regression model. For example,to reconstruct a digital breast tomosynthesis (DBT) projection, theprocess starts with the regression model trainer 402 training aregression model. At block 504, the regression model trainer 402 (FIGS.4A-4E) deploys the regression model. In this example, after theregression model has been trained, the regression model is deployed tothe voxel reconstructor 434 or the pixel reconstructor 452. DBTprojections data and a voxel 312 or a pixel 314 (FIGS. 3A-3E) are alsosent to the voxel reconstructor 434 or the pixel reconstructor 452. Atblock 506, the voxel reconstructor 434 or the pixel reconstructor 452uses the regression model for reconstruction. In the illustratedexample, the voxel reconstructor 434 or the pixel reconstructor 452 usesthe deployed regression model and the DBT projections data toreconstruct the voxel 312 or the pixel 314 sent by the voxel identifier432 or the pixel identifier 450 (FIGS. 4A-4E). At block 508, thereconstructed value producer 442 provides an output of a reconstructedimage value. For example, the reconstructed value producer 442 (FIGS.4A-4E) produces a reconstructed image value of the breast from the DBTprojections data. Example implementations of blocks 502, 504, 506, 508,are described in more detail below.

FIG. 6 is a flowchart representative of an example implementation oftraining a regression model (block 502 of FIG. 5 ). At block 602, theregression model trainer 402 determines if digital anthropomorphicphantoms (DAPs) are available to the regression model trainer 402. IfDAPs are available to the regression model trainer 402 at block 604, theregression model trainer 402 is instructed to train the regression modelon the DAP modeler 404 using a database composed of DAPs. An example oftraining a regression model on the DAP modeler 404 is further describedwith respect to FIG. 7 . In some examples, if the regression modeltrainer has DAPs for a regression model, then the regression model istrained on the DAP modeler 404. In these examples, the regression modeltrainer 402 checks for DAPs first. However, in other examples, theregression model trainer 402 may check for CT reconstruction data orimaging acquisitions that have been reconstructed with a given algorithmbefore checking for DAPs.

After the regression model trainer 402 is instructed to utilize the DAPmodeler 404, or if DAPs were not available at block 602, then at blocks606 and 608 respectively, the regression model trainer 402 is instructedto determine if computed tomography (CT) data is available. If CT datais available, then, at block 610, the regression model trainer 402 isinstructed to train the regression model on the CT modeler 406 using adatabase composed of CT reconstruction data. An example of training aregression model on a database composed of CT reconstruction data isfurther described with respect to FIG. 8 . In some examples, theregression model trainer 402 may have DAPs available to train aregression model. In such examples, after the regression model trainer402 instructs the DAP modeler 404 to train the regression model (block604), the regression model trainer 402 checks if there is CTreconstruction data available to train the regression model (block 606).If CT reconstruction data is available, the regression model is trainedon the CT modeler 406 (block 610). In further examples, the regressionmodel trainer 402 may not have had DAPs available to train a regressionmodel. In such examples, the regression model trainer checks if there isCT reconstruction data available to train the regression model (block608). If CT reconstruction data is available, the regression model istrained on the CT modeler 406 (block 610). In these illustratedexamples, the regression model trainer 402 checks for CT reconstructiondata (blocks 606, 608) after the regression model trainer 402 checks forDAPs (block 602) and before the regression model trainer 402 checks forimaging acquisitions that have been reconstructed with a given algorithm(block 612). However, in other examples, the regression model trainer402 may check for CT reconstruction data first or last.

After the regression model trainer 402 is instructed to train theregression model using the CT modeler 406 (block 610); or if CTreconstruction data was not available, but DAPs were available at block602, then the regression model trainer 402 determines if imagingacquisitions that have been reconstructed with a given algorithm areavailable at block 612. If imaging acquisitions that have beenreconstructed with a given algorithm are available, and/or if neitherDAPs nor CT reconstruction data were available at blocks 602 and 608respectively, then, at block 614, the regression model trainer 402 isinstructed to use a regression model that is trained on the algorithmmodifier 408 using a database composed of imaging acquisitions that havebeen reconstructed with a given algorithm. An example of training aregression model on the algorithm modifier 408 is further described withrespect to FIG. 9 . In some examples, the regression model trainer 402has access to CT reconstruction data. In such examples, after theregression model trainer 402 is instructed to use the CT modeler 406 totrain the regression model (block 610), the regression model trainer 402determines if imaging acquisitions that have been reconstructed with agiven algorithm are available (block 612). If imaging acquisitions thathave been reconstructed with a given algorithm are available, then theregression model trainer 402 trains the regression model on thealgorithm modifier 408 (block 614). In further examples, the regressionmodel trainer 402 may not have access to CT reconstruction data, butdoes have access to DAPs. In these examples, after instructing the DAPmodeler 404 to train the regression model (block 606) and afterconfirming that CT reconstruction data is unavailable, the regressionmodel trainer 402 determines if imaging acquisitions that have beenreconstructed with a given algorithm are available (block 612). Ifimaging acquisitions that have been reconstructed with a given algorithmare available, then the regression model trainer 402 trains theregression model on the algorithm modifier 408 (block 614). In evenfurther examples, the regression model trainer 402 may not have hadaccess to CT reconstruction data or DAPs. In such examples, theregression model trainer 402 automatically instructs the algorithmmodifier 408 to train the regression model (block 614). In theseexamples, the assumption is made that if a regression model is receivedby the regression model trainer 402, then the regression model trainer402 also receives at least one of DAPs, CT reconstruction data, orimaging acquisitions that have been reconstructed using a givenalgorithm. However, in other examples, the regression model trainer 402may not receive any of the DAPs, CT reconstruction data, or the imagingacquisitions that have been reconstructed using a given algorithm. Insuch examples, an error message shows on the user interface 449 of FIGS.4A-4E as the regression model cannot be trained.

After the regression model trainer 402 is instructed to train theregression model on the algorithm modifier 408 (block 614), the processreturns to block 504 of FIG. 5 . Additionally, if DAPs and/or CTreconstruction data are available, but imaging acquisitions that havebeen reconstructed with a given algorithm are not available, then theprocess returns to block 504 of FIG. 5 . For example, if the regressionmodel trainer 402 instructs the algorithm modifier 408 to train theregression model, then the process returns to block 504 of FIG. 5 . Infurther examples, if the regression model trainer 402 instructs the DAPmodeler 404 and/or the CT modeler 406 to train the regression model, butimaging acquisitions that have been reconstructed with a given algorithmare not available to the regression model trainer 402, then the programreturns to block 504 of FIG. 5 .

FIG. 7 is a flowchart representative of an example implementation ofusing a regression model that is trained on a database composed of DAPsused to simulate imaging acquisitions (block 604 of FIG. 6 ). At block702, the regression model trainer 402 (FIGS. 4A-4E) accesses a digitalversion of an image and several alternatives. For example, theregression model trainer 402 accesses a digital 3D breast that requiresreconstruction. In some examples, the regression model trainer 402 isgiven the acquisition of the image by the reconstruction controller 301,the voxel reconstructor 434, or the pixel reconstructor 452. However, inother examples, the regression model trainer 402 requests theacquisition of the image from the reconstruction controller 301, thevoxel reconstructor 434, or the pixel reconstructor 452. At block 704,the acquisition simulator 410 (FIGS. 4A-4E) within the DAP modeler 404simulates the image while maintaining access to the original 3D image.In this example, the regression model trainer 402 maintains access tothe original 3D image of the breast, and also simulates the image on theDAP acquisition simulator 410. At block 706, the DAP acquisitionsimulator 410 performs a simulation of imaging acquisitions from the 3Ddigital image and use the data as “grand proof.” In the illustratedexample, the simulation of the original 3D image of the breast is usedas grand proof. At block 708, the regression model trainer 402 performsregressions by training the model to get from the simulated imagingacquisitions to the original 3D phantom. For example, the regressionmodel trainer 402 performs regressions to get from simulated DBTacquisitions to the original 3D phantom. At block 710, the DAP algorithmcreator 414 designs an algorithm that gives the best possible mappingfunction from the imaging acquisitions to the 3D reconstructed image. Inthis example, the best possible mapping from the DBT acquisitions to theoriginal 3D phantom is used to design a new algorithm. At block 712, theDAP modeler 404 outputs the regression model based on the designedalgorithm. For example, the trained regression model based on thedesigned algorithm from block 710 is used to reconstruct a voxel 312 ora pixel 314 (FIGS. 3A-3E) in the voxel reconstructor 434 or the pixelreconstructor 452.

FIG. 8 is a flowchart representative of an example implementation ofusing a regression model that is trained on a database of CTreconstructed data to simulate imaging acquisitions (block 610 of FIG. 6). At block 802, the regression model trainer 402 (FIGS. 4A-4E) accessesan acquisition of an image that has been performed with a computedtomography (CT) scan. For example, the regression model trainer 402accesses a digital 3D breast that requires reconstruction. In someexamples, the regression model trainer 402 is given the acquisition ofthe image by the reconstruction controller 301, the voxel reconstructor434, or the pixel reconstructor 452. However, in other examples, theregression model trainer 402 requests the acquisition of the image fromthe reconstruction controller 301, the voxel reconstructor 434, or thepixel reconstructor 452. At block 804, the CT acquisition simulator 416within the CT modeler 406 simulates the image while maintaining accessto the original image in the CT scan. In this example, the regressionmodel trainer 402 maintains access to the original image of the 3Dbreast, and also simulates the image on the CT acquisition simulator416. At block 806, the CT acquisition simulator 416 performs asimulation of imaging acquisitions from the CT scan and use the data as“grand proof” In the illustrated example, the simulation of the original3D breast is used as grand proof. At block 808, the regression modeltrainer 402 performs regressions by training the model to get fromsimulated imaging acquisitions to the original CT scan. For example, theregression model trainer 402 performs regressions to get from simulatedDBT acquisitions to the original CT scan. At block 810, the CT algorithmcreator 420 within the CT modeler 406 designs an algorithm that givesthe best possible mapping function from the imaging acquisitions to the3D reconstructed image. In this example, the best possible mapping fromthe DBT acquisitions to the original CT scan is used to design a newalgorithm. At block 812, the CT modeler 406 outputs the regression modelbased on the designed algorithm of block 810. For example, the trainedregression model based on the algorithm designed at block 810 is used toreconstruct a voxel 312 or a pixel 314 (FIGS. 3A-3E) in the voxelreconstructor 434 or the pixel reconstructor 452.

FIG. 9 is a flowchart representative of an example detailed breakdown ofblock 614 of FIG. 6 . At block 614, the reconstruction controller 301decides to use a regression model that is trained on the algorithmmodifier 408. At block 902, the regression model trainer 402 (FIGS.4A-4E) accesses an existing imaging algorithm from the algorithmdatabase 422 that manages noise artifacts in an image to give high imagequality. For example, the regression model trainer 402 accesses a DBTalgorithm (e.g., ASiR, MBIR, etc.). At block 904, the acquisitionreconstructor 424 within the algorithm modifier 408 estimates areconstructed algorithm with the neural network to reduce computationalcomplexity of the original algorithm to produce the same image faster.In this example, the neural network reduces the computational power ofthe DBT algorithm. At block 906, the regression model trainer 402 trainsthe regression model using the new algorithm to decrease computationtime and computation complexity. In the illustrated example, the neuralnetwork reduces the computational power of the DBT algorithm. As aresult, the same reconstructed image is obtained faster. At block 908,the algorithm modifier 408 outputs the regression model based on thereconstructed algorithm. For example, the trained regression model basedon the reconstructed algorithm is used to reconstruct a voxel 312 or apixel 314 (FIGS. 3A-3E) in the voxel reconstructor 434 or the pixelreconstructor 452.

FIG. 10 is a flowchart representative of an example implementation ofdeploying a regression model (block 504 of FIG. 5 ). At block 1002, thevoxel reconstructor 434 or the pixel reconstructor 452 (FIGS. 4A-4E) isgiven a set of data from the imaging projections data receiver 430, thevolume receiver 456, the orientation parameter receiver 460, and/or thethickness parameter receiver 462 and a voxel 312 or a pixel 314 (FIGS.3A-3E) to reconstruct from the voxel identifier 432 or the pixelidentifier 450. For example, the voxel reconstructor 434 may be given aset of DBT projections data from the imaging projections data receiver430 and a voxel to reconstruct from the voxel identifier 432. At block1004, the reconstruction controller 301 chooses which regression modelto use. In this example, the reconstruction controller 301 decides touse a regression model trained on the DAP modeler 404, the CT modeler406, and/or the algorithm modifier 408. At block 1006, the voxelprojector 436 within the voxel reconstructor 434 or the pixel mapper 454within the pixel reconstructor 452 uses the regression model to map aset of pixel values to a voxel or another pixel value. The process ofmapping a set of pixel values to a voxel or another pixel value wasdescribed in detail in FIGS. 1A-2B. In the illustrated example, theregression model trained in the regression model trainer 402 is used tomap a set of pixel values to a voxel value. In other examples, a set ofpixel values may be mapped to another pixel value to create a synthetic2D reconstruction.

FIG. 11 is a flowchart representative of an example implementation ofusing a regression model for reconstruction (block 506 of FIG. 5 ). Atblock 1102, the reconstructor 306 determines if imaging projections arereceived. If so, at block 1104, the voxel projector 436, the pixelmapper 454, or the voxel mapper 464 projects or maps a voxel 312 or apixel 314 (FIGS. 3A-3E) to be reconstructed onto each imaging projectionaccording to an acquisition geometry. For example, a voxel may beprojected onto each 2D DBT projection according to the original breastacquisition geometry. This process was previously described inconnection with FIGS. 1A-2B. At block 1106, the adjacent pixel extractor438 and/or the adjacent voxel extractor 458 extracts adjacent pixelsand/or adjacent voxels around each projected pixel or voxel. In thisexample, adjacent pixels around each projected pixel in the voxel areextracted. At block 1108, the reconstructor 306 decides if another voxel312 or pixel 314 is to be reconstructed. If yes, the process repeatsstarting at block 1102. In the illustrated example, if there aremultiple voxels that require reconstruction, then the process startsover with block 1102. If no, or if imaging projections were notreceived, the reconstructor 306 determines if a volume is received atblock 1110. If yes, at block 1112, the voxel projector 436, the pixelmapper 454, or the voxel mapper 464 projects or maps a voxel 312 or apixel 314 (FIGS. 3A-3E) to be reconstructed onto each imaging projectionaccording to an acquisition geometry. At block 1114, the adjacent pixelextractor 438 and/or the adjacent voxel extractor 458 extracts adjacentvoxels and/or adjacent pixels around the mapped pixel, voxel, or slab.At block 1116, the reconstructor 306 determines if another voxel 312 orpixel 314 is to be reconstructed. If yes, the process repeats startingat block 1110. If no, the process is finished and returns to block 508of FIG. 5 .

FIG. 12 is a flowchart representative of an example implementation ofproviding an output reconstructed image (block 508 of FIG. 5 ). At block1202, the voxel reconstructor 434 or the pixel reconstructor 452reconstructs all voxels 312 and/or pixels 314 (FIGS. 3A-3E) that requirereconstruction. For example, if there are 3 voxels in a DBT projectionsdata simulation that require reconstruction, then the voxelreconstructor 434 reconstructs all 3 voxels. At block 1204, theregression model feeder 440 feeds the regression model with extractedreconstruction data to produce a reconstructed value of the pixelsand/or voxels at the reconstructed value producer 442. For example, theregression model feeder 440 may feed the regression model with extractedreconstruction data through an artificial neural network (such as aconvolutional neural network (CNN), recurrent neural network (RNN),feedforward neural network, etc.), a regression support vector machine(SVM), etc. In the illustrated example, the regression model is fed withextracted voxel reconstruction data to produce a reconstructed value ofthe voxels in the model of the breast. At block 1206, a reconstructedimage is produced formed by example reconstructed image producer 444using the reconstructed values (e.g., gray values, etc.) of the voxelsand/or pixels. In this example, a 3D reconstructed image of the breastis formed by utilizing the reconstructed values of the voxels and/orpixels.

FIG. 13 is a block diagram of an example processor platform 1300 capableof executing the instructions of FIGS. 5-12 to implement the examplesystem 300 of FIGS. 4A-4E. The processor platform 1300 can be, forexample, a server, a personal computer, a mobile device (e.g., a cellphone, a smart phone, a tablet such as an iPad™), a personal digitalassistant (PDA), an Internet appliance, a DVD player, a CD player, adigital video recorder, a Blu-ray player, a gaming console, a personalvideo recorder, a set top box, or any other type of computing device.

The processor platform 1300 of the illustrated example includes aprocessor 1312. The processor 1012 of the illustrated example ishardware. For example, the processor 1312 can be implemented by one ormore integrated circuits, logic circuits, microprocessors or controllersfrom any desired family or manufacturer.

The processor 1312 of the illustrated example includes a local memory1313 (e.g., a cache). The processor 1312 of the illustrated example isin communication with a main memory including a volatile memory 1314 anda non-volatile memory 1316 via a bus 1318. The volatile memory 1314 maybe implemented by Synchronous Dynamic Random Access Memory (SDRAM),Dynamic Random Access Memory (DRAM), RAMBUS Dynamic Random Access Memory(RDRAM) and/or any other type of random access memory device. Thenon-volatile memory 1316 may be implemented by flash memory and/or anyother desired type of memory device. Access to the main memory 1314,1316 is controlled by a memory controller.

The processor platform 1300 of the illustrated example also includes aninterface circuit 1320. The interface circuit 1320 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 1322 are connectedto the interface circuit 1320. The input device(s) 1322 permit(s) a userto enter data and commands into the processor 1012. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, isopoint and/or a voice recognition system.

One or more output devices 1324 are also connected to the interfacecircuit 1320 of the illustrated example. The output devices 1024 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a printer and/or speakers). The interface circuit 1320 ofthe illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor.

The interface circuit 1320 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network1326 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 1300 of the illustrated example also includes oneor more mass storage devices 1328 for storing software and/or data.Examples of such mass storage devices 1328 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAIDsystems, and digital versatile disk (DVD) drives.

The coded instructions 1332 of FIGS. 4A-4E may be stored in the massstorage device 1328, in the volatile memory 1314, in the non-volatilememory 1316, and/or on a removable tangible computer readable storagemedium such as a CD or DVD.

From the foregoing, it will appreciate that the above disclosed methods,apparatus and articles of manufacture facilitate improved imagereconstruction and generation of 2D and/or 3D images from projectiondata, such as DBT projection data. Certain examples facilitate improvedmodeling of image information to facilitate synthetic 2D imagegeneration from available projection information. Certain examplesalleviate dependence on particular equations to instead leveragemodeling and learning to generate 2D and/or 3D images from availableimage projection information. Certain examples facilitate improvedapplication of artificial intelligence techniques to imagereconstruction. Certain examples provide technological improvement toprocessors configured for modeling, processing, and reconstruction ofimage data, such as 2D and/or 3D images generated from image projectiondata (e.g., DBT, etc.), etc.

For example, in DBT/CE-DBT, reconstruction directly impacts content ofthe data for radiologists to review, and, therefore, impacts a resultingdiagnosis. While today's algorithms tend to optimize the quality ofreconstructed slices (e.g., reducing the noise, mitigating streakingartifacts, etc.), a prior knowledge introduced in these algorithmsusually only partially address defects resulting in non-perfectreconstructed data. Additionally, these sophisticated algorithms areusually complex and require significant computational power.Consequently, the design of an ideal reconstruction is limited by theknow-how of the algorithm designer. However, for a given voxel, areconstruction algorithm can simply be seen as a mapping function thatassociates a reconstructed gray level to a set of input gray levelsextracted from the projections.

Thus, certain examples approximate any reconstruction algorithm usingregression tools. Certain examples bring a technological improvement toprocessor reconstruction by learning “ideal” reconstruction that wouldotherwise be almost impossible to model. Certain examples allowsimplifying the design of reconstruction algorithms. For example,computational effort can be lowered by approximating existingalgorithms. Additionally, certain examples provide a radiologist withmore relevant reconstructed volumes by designing/learning algorithmsthat would otherwise be difficult to model (e.g., learn groundtruth/perfect data, etc.).

Although certain example methods, apparatus and articles of manufacturehave been disclosed herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

What is claim is:
 1. A system comprising: a regression model trainer totrain a regression model, the regression model trained usingthree-dimensional (3D) volume data and at least one of acquiredtwo-dimensional (2D) projection data or simulated 2D projection data anddeployed to reconstruct image pixels to form a reconstructed image; apixel identifier to identify a pixel to be reconstructed; a volumereceiver to receive a first volume; and a pixel reconstructor including:a pixel mapper to map the pixel onto voxels from the first volumeaccording to an acquisition geometry, the acquisition geometryassociated with a particular path or movement of an x-ray source withrespect to a 3D object to obtain a series of 2D projections; an adjacentvoxel extractor to extract adjacent voxels around each mapped pixel ofthe image pixels; and a regression model feeder to feed the regressionmodel with the extracted adjacent voxels to produce a reconstructedvalue of the pixel.
 2. The system of claim 1, wherein the regressionmodel trainer includes: a database including acquired projection dataand a 2D mammogram acquired under the same compression, the regressionmodel trained to output a 2D image approximately identical to the 2Dmammogram when fed with the projections; or a database includingsimulated projection data and a simulated 2D mammogram acquired underthe same compression from a digital anthropomorphic phantom, theregression model trained to output a 2D image approximately identical tothe simulated 2D mammogram when fed with the simulated projections. 3.The system of claim 1, wherein the regression model trainer includes: aDigital Anthropomorphic Phantom (DAP) Modeler including an acquisitionsimulator, an algorithm creator, and a DAP database; a ComputedTomography (CT) Modeler including an acquisition simulator, an algorithmcreator, and a CT database; and an Algorithm Modifier including anacquisition reconstructor and an algorithm database.
 4. The system ofclaim 1, further including a feedback generator to identify when amistake has been made on the reconstructed image and, when the mistakeis identified, to communicate to the regression model trainer tore-train the regression model.
 5. The system of claim 1, furtherincluding a reconstructed value producer to produce a reconstructedvalue for each pixel of the image pixels to be reconstructed, thereconstructed values used to produce the reconstructed image.
 6. Thesystem of claim 1, further including a user interface, the userinterface to display the reconstructed image pixels.
 7. A non-transitorycomputer readable storage medium comprising instructions which, whenexecuted, cause a processor to at least: receive a first volume;identify a pixel to reconstruct; receive a trained regression model, theregression model trained using three-dimensional (3D) volume data and atleast one of acquired two-dimensional (2D) projection data or simulated2D projection data and deployed to reconstruct image pixels to form areconstructed image; and reconstruct the pixel by: mapping the pixelonto voxels from the first volume according to an acquisition geometry,the acquisition geometry associated with a particular path or movementof an x-ray source with respect to a 3D object to obtain a series of 2Dprojections; extracting adjacent voxels around each mapped pixel of theimage pixels; feeding the regression model with the extracted adjacentvoxels to produce a reconstructed value of the pixel; and repeating thereconstruction for each pixel of the image pixels to be reconstructed.8. The non-transitory computer readable storage medium of claim 7,wherein the regression model is trained on at least one of: a databaseincluding acquired projection data and a 2D mammogram acquired under thesame compression, the regression model trained to output a 2D imageapproximately identical to the 2D mammogram when fed with theprojections; or a database including simulated projection data and asimulated 2D mammogram acquired under the same compression from adigital anthropomorphic phantom, the regression model trained to outputa 2D image approximately identical to the simulated 2D mammogram whenfed with the simulated projections.
 9. The non-transitory computerreadable storage medium of claim 7, wherein the regression model istrained on at least one of: a database including digital anthropomorphicphantoms and simulated projection data obtained from the phantoms for agiven acquisition geometry, the regression model trained to output asecond volume approximately identical to the anthropomorphic phantomwhen fed with the simulated projections; a database including computedtomography (CT) reconstructed data and simulated projections dataobtained from the CT reconstruction data, the regression model trainedto output a third volume approximately identical to the CT reconstructeddata when fed with the simulated projections; or a database includingacquired projection data and reconstructed data from these projectiondata with a given reconstruction algorithm, the regression model trainedto output a fourth volume approximately identical to the reconstructeddata when fed with the acquired projections.
 10. The non-transitorycomputer readable storage medium of claim 7, further includinginstructions which, when executed, cause a machine to identify a mistakewithin the reconstructed image and, when the mistake is identified, tore-train the regression model.
 11. The non-transitory computer readablestorage medium of claim 7, further including instructions which, whenexecuted cause a machine to produce the reconstructed image onto a userinterface using the reconstructed pixel values.
 12. A method comprising:receiving a set of imaging projection data; receiving a first volume;identifying a pixel to reconstruct; receiving a trained regressionmodel, the regression model trained using three-dimensional (3D) volumedata and at least one of acquired two-dimensional (2D) projection dataor simulated 2D projection data and deployed to reconstruct imagepixels; and reconstructing the pixel by: mapping the pixel onto eachimaging projection in the set of projections according to an acquisitiongeometry; mapping the pixel onto voxels from the first volume accordingto an acquisition geometry, the acquisition geometry associated with aparticular path or movement of an x-ray source with respect to a 3Dobject to obtain a series of 2D projections; extracting adjacent pixelsaround each mapped pixel of the image pixels in the projections;extracting adjacent voxels around each mapped pixel of the image pixelsin the first volume; feeding the regression model with the extractedadjacent pixels and extracted adjacent voxels to produce a reconstructedvalue of the pixel; and repeating the reconstruction for each pixel ofthe image pixels to be reconstructed.
 13. The method of claim 12,further including training the regression model on at least one of: adatabase including acquired projection data and a 2D mammogram acquiredunder the same compression, the regression model trained to output a 2Dimage approximately identical to the 2D mammogram when fed with theprojections; or a database including simulated projection data and asimulated 2D mammogram acquired under the same compression from adigital anthropomorphic phantom, the regression model trained to outputa 2D image approximately identical to the simulated 2D mammogram whenfed with the simulated projections.
 14. The method of claim 12, furtherincluding training the regression model on at least one of: a databaseincluding digital anthropomorphic phantoms and simulated projection dataobtained from the phantoms for a given acquisition geometry, theregression model trained to output a second volume approximatelyidentical to the anthropomorphic phantom when fed with the simulatedprojections; a database including computed tomography (CT) reconstructeddata and simulated projections data obtained from the CT reconstructiondata, the regression model trained to output a third volumeapproximately identical to the CT reconstructed data when fed with thesimulated projections; or a database including acquired projection dataand reconstructed data from these projection data with a givenreconstruction algorithm, the regression model trained to output afourth volume approximately identical to the reconstructed data when fedwith the acquired projections.
 15. The method of claim 12, furtherincluding displaying a reconstructed image onto a user interface usingthe reconstructed values.
 16. A non-transitory computer readable storagemedium comprising instructions which, when executed, cause a processorto at least: receive a set of imaging projections data; receive a firstvolume; identify a pixel to reconstruct; receive a trained regressionmodel, the regression model trained using three-dimensional (3D) volumedata and at least one of acquired two-dimensional (2D) projection dataor simulated 2D projection data and deployed to reconstruct image pixelsto form a reconstructed image; and reconstruct the pixel by: mapping thepixel onto each imaging projection in the set of imaging projectionsaccording to an acquisition geometry, the acquisition geometryassociated with a particular path or movement of an x-ray source withrespect to a 3D object to obtain a series of 2D projections; mapping thepixel onto voxels from the first volume according to an acquisitiongeometry; extracting adjacent pixels around each mapped pixel of theimage pixels in the projections; extracting adjacent voxels around themapped pixel of the image pixels in the first volume; feeding theregression model with the extracted adjacent pixels and the extractedadjacent voxels to produce a reconstructed value of the pixel; andrepeating the reconstruction for each pixel of the image pixels to bereconstructed.
 17. The non-transitory computer readable storage mediumof claim 16, wherein the regression model is trained on at least one of:a database including acquired projection data and a 2D mammogramacquired under the same compression, the regression model trained tooutput a 2D image approximately identical to the 2D mammogram when fedwith the projections; or a database including simulated projection dataand a simulated 2D mammogram acquired under the same compression from adigital anthropomorphic phantom, the regression model trained to outputa 2D image approximately identical to the simulated 2D mammogram whenfed with the simulated projections.
 18. The non-transitory computerreadable storage medium of claim 16, wherein the regression model istrained on at least one of: a database including digital anthropomorphicphantoms and simulated projection data obtained from the phantoms for agiven acquisition geometry, the regression model trained to output asecond volume approximately identical to the anthropomorphic phantomwhen fed with the simulated projections; a database including computedtomography (CT) reconstructed data and simulated projections dataobtained from the CT reconstruction data, the regression model trainedto output a third volume approximately identical to the CT reconstructeddata when fed with the simulated projections; or a database includingacquired projection data and reconstructed data from these projectiondata with a given reconstruction algorithm, the regression model trainedto output a fourth volume approximately identical to the reconstructeddata when fed with the acquired projections.
 19. The non-transitorycomputer readable storage medium of claim 16, further includinginstructions which, when executed, cause a machine to identify a mistakewithin the reconstructed image and to re-train the regression model. 20.The non-transitory computer readable storage medium of claim 16, furtherincluding instructions which, when executed cause a machine to producethe reconstructed image onto a user interface using the reconstructedpixels.